rounding off numbers problem solving

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Rounding Numbers Worksheet Rounding Challenges

Welcome to our Rounding Numbers Worksheet collection of Rounding Challenges. Here you will find a wide range of free printable math Worksheets, which will help your child learn to apply their rounding knowledge to solve a variety of rounding challenges.

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Rounding Numbers Worksheets

Rounding challengs.

Here you will find a range of selection of printable rounding challenges to give your child practice and consolidation with their rounding work.

These sheets are carefully graded so that the easier sheets come first.

Each challenge consists of 4 clues and 8 possible answers, of which only one is correct.

Children have to look at the clues and use them to work out the correct answer.

These activities can be used individually with children working through the challenges on their own, but they are also great for partner work, and children discussing and sharing their ideas, and developing their mathematical language.

Each sheets comes with a separate printable answer sheet.

Using these sheets will help your child to:

apply their rounding knowledge to solve problems;
solve mathematical problems;
develop children's vocabulary and understanding of the properties of numbers.

All the free Rounding challenges in this section support the Elementary Math Benchmarks.

Rounding Challenges to the nearest 10

Rounding Challenges 1
Rounding Challenges 1 Answers
PDF version
Rounding Challenges 2
Rounding Challenges 2 Answers

Rounding Challenges to the nearest 10 & 100

Rounding Challenges 3
Rounding Challenges 3 Answers
Rounding Challenges 4
Rounding Challenges 4 Answers

Rounding Challenges to the nearest 10, 100 & 1000

Rounding Challenges 5
Rounding Challenges 5 Answers
Rounding Challenges 6
Rounding Challenges 6 Answers

Looking for something harder?

The rounding decimals challenges in this section involve rounding decimal numbers to the nearest whole, tenth or 2dp.

They are at a more challenging level than those on this page, and involve decimals.

Rounding Decimals Worksheet Challenges

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

Rounding Off Worksheet Generator

Here is our generator for generating your own rounding off numbers worksheets.

Our generator will create the following worksheets:

rounding off to the nearest 10, 100, 1000 or 10000
rounding to the nearest whole, to 1dp, or 2dp.
rounding off to 1sf, 2sf or 3sf
Rounding Off Numbers Worksheets

How to Round whole numbers

learn to round numbers to the nearest 10, 100 or 1000.

Each of the webpages below comes with rounding help as well as practice worksheets.

Rounding to the nearest 10 Worksheets
Rounding to the nearest 100 worksheets
Rounding to the nearest 1000 worksheets
Rounding Decimals to the nearest whole

Online Rounding Practice Zone

In our Rounding Practice zone, you can practice rounding a range of numbers. You can round numbers to the nearest 10, 100 or even 1000. Want to round numbers to the nearest decimal place, you can do that too!

Select the numbers you want to practice with, and print out your results when you have finished.

You can also use the practice zone for benchmarking your performance, or using it with a group of children to gauge progress.

Rounding Practice Zone

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Rounding & Estimation Word Problems

Related Pages Math Worksheets Lessons for Fourth Grade Free Printable Worksheets

Printable “Rounding Numbers” Worksheets: Round Numbers using the Number Line Round to nearest 10 Round to nearest 100 Round to nearest 1000, 10000, 100000 Rounding Word Problems

Rounding Word Problems Worksheets

In these free math worksheets, students practice how to use rounding to estimate and check the answers to word problems.

How to use estimation or rounding? Estimation or rounding is a useful tool for checking answers because it allows you to quickly determine if an answer is reasonable or not.

Here are some steps you can follow to use estimation to check an answer: Step 1: Make sure you understand what you are being asked to find and what information you have been given. Step 2: Round any numbers given in the problem to the nearest whole number, or to the nearest ten, hundred, or thousand, depending on the level of accuracy needed. Step 3: Use mental math to perform calculations quickly. For example, if you need to add 23 and 45, round them both to 20 and 50 and add those instead. This will give you an estimate that is close to the actual answer. Step 4: Once you have an estimate, compare it to the actual answer you calculated. If the estimate is close to the actual answer, you can be confident that your calculation is correct. If the estimate is significantly different from the actual answer, you may need to review your work and make corrections.

By using estimation to check your answers, you can catch errors early and avoid making mistakes that could lead to incorrect results.

Click on the following worksheet to get a printable pdf document. Scroll down the page for more Rounding Word Problems Worksheets .

Related Lessons & Worksheets

Round to nearest 10 (2-digit) (eg. 45 -> 50) Round to nearest 10 (3-digit) (eg. 725 -> 730) Round to nearest 100 (3-digit) (eg. 651 -> 700) Round to nearest 10 or 100 (3-digit)

Round to nearest 100 (4-digit) (eg. 2,754 -> 2,800) Round to nearest 1000 (eg. 3,542 -> 4,000) Round to nearest 10, 100, 1000

Round the nearest thousands

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Rounding Worksheets

Rounding worksheets for grades 1-5.

Our rounding worksheets provide practice in rounding numbers to different place values (nearest ten, nearest 100, ...). In later grades the exercises are similar, but with larger numbers.

Choose your grade / topic:

Grade 1: Rounding worksheets

Grade 2: Rounding worksheets

Grade 3: Rounding worksheets

Grade 4: Rounding worksheets

Grade 5: Rounding worksheets

Topics include:

Grade 1 rounding worksheets

Rounding numbers to the nearest 10

Grade 2 rounding worksheets

Rounding numbers to the nearest 10 within 0-100
Rounding numbers to the nearest 10 within 0-1,000
Rounding numbers to the nearest 100 within 0-1,000
Rounding numbers to the nearest 10 or 100 within 0-1,000

Grade 3 rounding worksheets

Rounding numbers to the nearest 100 within 0-10,000
Mixed rounding - round to the underlined digit (10's, 100's)
Mixed rounding - round to the underlined digit (10's, 100's, 1000's)

Grade 4 rounding worksheets

Rounding numbers to the nearest 1,000 within 0-10,000
Rounding numbers to the nearest 10,000 within 0-1,000,000
Mixed rounding - round to the underlined digit
Estimating and rounding word problems

Grade 5 rounding worksheets

Rounding numbers to the nearest 10 within 0-10,000
Rounding numbers to the nearest 100 within 0-1,000,000
Rounding numbers to the nearest 1,000 within 0-1,000,000
Mixed rounding - round to the underlined digit (up to nearest million)

1.3: Rounding Whole Numbers

Last updated
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Page ID 48776

Denny Burzynski & Wade Ellis, Jr.
College of Southern Nevada via OpenStax CNX

Learning Objectives

understand that rounding is a method of approximation
be able to round a whole number to a specified position

Rounding as an Approximation

A primary use of whole numbers is to keep count of how many objects there are in a collection. Sometimes we're only interested in the approximate number of objects in the collection rather than the precise number. For example, there are approximately 20 symbols in the collection below.

$An arrangement of symbols.$

The precise number of symbols in the above collection is 18.

Definition: Rounding

We often approximate the number of objects in a collection by mentally seeing the collection as occurring in groups of tens, hundreds, thousands, etc. This process of approximation is called rounding . Rounding is very useful in estimation. We will study estimation in Chapter 8.

When we think of a collection as occurring in groups of tens, we say we're rounding to the nearest ten . When we think of a collection as occurring in groups of hundreds, we say we're rounding to the nearest hundred . This idea of rounding continues through thousands, ten thousands, hundred thousands, millions, etc.

The process of rounding whole numbers is illustrated in the following examples.

Example $\PageIndex{1}$

Round 67 to the nearest ten.

On the number line, 67 is more than halfway from 60 to 70. The digit immediately to the right of the tens digit, the round-off digit, is the indicator for this.

$A number line from 0 to 70. At the dash for the number sixty is a label, 6 tens. At the dash for 70 is a label, 7 tens. In between the two dashes is a dot on the number 67. Below, is a statement. 67 is closer to 7 tens than it is to 6 tens.$

Thus, 67, rounded to the nearest ten, is 70.

Example $\PageIndex{2}$

Round 4,329 to the nearest hundred.

On the number line, 4,329 is less than halfway from 4,300 to 4,400. The digit to the immediate right of the hundreds digit, the round-off digit, is the indicator.

$A number line from 0 to 4,400. The mark for 4,300 is labeled, 3 hundreds. The mark for 4,400 is labeled, 4 hundreds. A dot on the number 4,329 is in between the two marks. Below the number line is a statement. 4,329 is closer to 43 hundreds than it is to 44 hundreds.$

Thus, 4,329, rounded to the nearest hundred is 4,300.

Example $\PageIndex{3}$

Round 16,500 to the nearest thousand.

On the number line, 16,500 is exactly halfway from 16,000 to 17,000.

$A number line from 0 to 17,000. The 16,000 mark is labeled, 6 thousands. The 17,000 mark is labeled, 7 thousands. In between the two marks is a dot on the number 16,500.$

By convention, when the number to be rounded is exactly halfway between two numbers, it is rounded to the higher number.

Thus, 16,500, rounded to the nearest thousand, is 17,000.

Example $\PageIndex{4}$

A person whose salary is $41,450 per year might tell a friend that she makes $41,000 per year. She has rounded 41,450 to the nearest thousand. The number 41,450 is closer to 41,000 than it is to 42,000.

The Method of Rounding Whole Numbers

From the observations made in the preceding examples, we can use the following method to round a whole number to a particular position.

Mark the position of the round-off digit.
If it is less than 5, replace it and all the digits to its right with zeros. Leave the round-off digit unchanged.
If it is 5 or larger, replace it and all the digits to its right with zeros. Increase the round-off digit by 1.

Sample Set A

Use the method of rounding whole numbers to solve the following problems.

Round 3,426 to the nearest ten.

$3,426, with the 2 labeled, tens position.$

Observe the digit immediately to the right of the tens position. It is 6. Since 6 is greater than 5, we round up by replacing 6 with 0 and adding 1 to the digit in the tens position (the round-off position): 2+1=32+1=3 . 3,430

Thus, 3,426 rounded to the nearest ten is 3,430.

Round 9,614,018,007 to the nearest ten million.

$9,614,018,007, with the first 1 labeled, ten millions position.$

Observe the digit immediately to the right of the ten millions position. It is 4. Since 4 is less than 5, we round down by replacing 4 and all the digits to its right with zeros. 9,610,000,000

Thus, 9,614,018,007 rounded to the nearest ten million is 9,610,000,000.

Round 148,422 to the nearest million.

$0,148,422, with the 0 labeled, millions position.$

The digit immediately to the right is 1. Since 1 is less than 5, we'll round down by replacing it and all the digits to its right with zeros. 0,000,000 This number is 0.

Thus, 148,422 rounded to the nearest million is 0.

Round 397,000 to the nearest ten thousand.

$397,000, with the 9 labeled, ten thousand position.$

The digit immediately to the right of the ten thousand position is 7. Since 7 is greater than 5, we round up by replacing 7 and all the digits to its right with zeros and adding 1 to the digit in the ten thousands position. But 9+1=109+1=10 and we must carry the 1 to the next (the hundred thousands) position. 400,000

Thus, 397,000 rounded to the nearest ten thousand is 400,000.

Practice Set A

Use the method of rounding whole numbers to solve each problem.

Round 3387 to the nearest hundred.

Round 26,515 to the nearest thousand.

Round 30,852,900 to the nearest million.

Round 39 to the nearest hundred.

Round 59,600 to the nearest thousand.

For the following problems, complete the table by rounding each number to the indicated positions.

Exercise $\PageIndex{1}$

Exercise $\PageIndex{2}$

Exercise $\PageIndex{3}$

Exercise $\PageIndex{4}$

Exercise $\PageIndex{5}$

Exercise $\PageIndex{6}$

Exercise $\PageIndex{7}$

Exercise $\PageIndex{8}$

Exercise $\PageIndex{9}$

Exercise $\PageIndex{10}$

Exercise $\PageIndex{11}$

Exercise $\PageIndex{12}$

Exercise $\PageIndex{13}$

551,061,285

Exercise $\PageIndex{14}$

23,047,991,521

Exercise $\PageIndex{15}$

106,999,413,206

Exercise $\PageIndex{16}$

Exercise $\PageIndex{17}$

Exercise $\PageIndex{18}$

Exercise $\PageIndex{19}$

Exercise $\PageIndex{20}$

Exercise $\PageIndex{21}$

Exercise $\PageIndex{22}$

Exercise $\PageIndex{23}$

Exercise $\PageIndex{24}$

In 1950, there were 5,796 cases of diphtheria reported in the United States. Round to the nearest hundred.

Exercise $\PageIndex{25}$

In 1979, 19,309,000 people in the United States received federal food stamps. Round to the nearest ten thousand.

Exercise $\PageIndex{26}$

In 1980, there were 1,105,000 people between 30 and 34 years old enrolled in school. Round to the nearest million.

Exercise $\PageIndex{27}$

In 1980, there were 29,100,000 reports of aggravated assaults in the United States. Round to the nearest million.

For the following problems, round the numbers to the position you think is most reasonable for the situation.

Exercise $\PageIndex{28}$

In 1980, for a city of one million or more, the average annual salary of police and firefighters was $16,096.

Exercise $\PageIndex{29}$

The average percentage of possible sunshine in San Francisco, California, in June is 73%.

Exercise $\PageIndex{30}$

In 1980, in the state of Connecticut, $3,777,000,000 in defense contract payroll was awarded.

Exercise $\PageIndex{31}$

In 1980, the federal government paid $5,463,000,000 to Viet Nam veterans and dependants.

$5,500,000,000

Exercise $\PageIndex{32}$

In 1980, there were 3,377,000 salespeople employed in the United States.

Exercise $\PageIndex{33}$

In 1948, in New Hampshire, 231,000 popular votes were cast for the president.

Exercise $\PageIndex{34}$

In 1970, the world production of cigarettes was 2,688,000,000,000.

Exercise $\PageIndex{35}$

In 1979, the total number of motor vehicle registrations in Florida was 5,395,000.

Exercise $\PageIndex{36}$

In 1980, there were 1,302,000 registered nurses the United States.

Exercises for Review

Exercise $\PageIndex{37}$

There is a term that describes the visual displaying of a number. What is the term?

Exercise $\PageIndex{38}$

What is the value of 5 in 26,518,206?

Exercise $\PageIndex{39}$

Write 42,109 as you would read it.

Forty-two thousand, one hundred nine

Exercise $\PageIndex{40}$

Write "six hundred twelve" using digits.

Exercise $\PageIndex{41}$

Write "four billion eight" using digits.

4,000,000,008

Rounding Numbers

What is "rounding" .

Rounding means making a number simpler but keeping its value close to what it was.

The result is less accurate, but easier to use.

Example: 73 rounded to the nearest ten is 70 , because 73 is closer to 70 than to 80. But 76 goes up to 80.

Common Method

There are several different methods for rounding . Here we look at the common method , the one used by most people:

"5 or more rounds up"

First some examples (explanations follow):

How to Round Numbers

Decide which is the last digit to keep
Leave it the same if the next digit is less than 5 (this is called rounding down )
But increase it by 1 if the next digit is 5 or more (this is called rounding up )

Example: Round 74 to the nearest 10

We want to keep the "7" (it is in the 10s position)
The next digit is "4" which is less than 5, so no change is needed to "7"

(74 gets "rounded down")

Example: Round 86 to the nearest 10

We want to keep the "8"
The next digit is "6" which is 5 or more, so increase the "8" by 1 to "9"

(86 gets "rounded up")

When the first digit removed is 5 or more, increase the last digit remaining by 1.

Why does 5 go up ?

5 is in the middle ... so we could go up or down. But we need a method that everyone agrees to.

Think about sport: we should have the same number of players on each team, right?

And that is the "common" method of rounding. Read about other methods of rounding .

A farmer counted 87 cows in the field, but when he rounded them up he had 90.

Rounding Decimals

First work out which number will be left when we finish.

Rounding to tenths means to leave one number after the decimal point.
Rounding to hundredths means to leave two numbers after the decimal point.

3.1416 rounded to hundredths is 3.14

as the next digit (1) is less than 5

3.1416 rounded to thousandths is 3.142

as the next digit (6) is more than 5

1.2735 rounded to tenths is 1.3

as the next digit (7) is 5 or more

To round to "so many decimal places" count that many digits from the decimal point:

1.2735 rounded to 3 decimal places is 1.274

as the next digit (5) is 5 or more

Rounding Whole Numbers

We may want to round to tens, hundreds, etc, In this case we replace the removed digits with zero.

134.9 rounded to tens is 130

as the next digit (4) is less than 5

12,690 rounded to thousands is 13,000

as the next digit (6) is 5 or more

15.239 rounded to ones is 15

as the next digit (2) is less than 5

Rounding to Significant Digits

To round to "so many" significant digits, count digits from left to right , and then round off from there.

1.239 rounded to 3 significant digits is 1.24

as the next digit (9) is 5 or more

134.9 rounded to 1 significant digit is 100

as the next digit (3) is less than 5

When there are leading zeros (such as 0.006), don't count them because they are only there to show how small the number is:

0.0165 rounded to 2 significant digits is 0.017

Significant digit calculator.

(Try increasing or decreasing the number of significant digits. Also try numbers with lots of zeros in front of them like 0.00314, 0.0000314 etc)

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Rounding Off Numbers Problem Solving

Rounding Off Numbers Problem Solving - Displaying top 8 worksheets found for this concept.

Some of the worksheets for this concept are Lesson plan rounding off, Rounding, Problem solving rounding and estimating, Rounding decimals introduction packet, Word problems involving rounding yr6, 1 rounding numbers, Rounding decimal places and significant figures, Round each number to the nearest 10.

Found worksheet you are looking for? To download/print, click on pop-out icon or print icon to worksheet to print or download. Worksheet will open in a new window. You can & download or print using the browser document reader options.

1. LESSON PLAN: Rounding off

2. rounding, 3. problem solving: rounding and estimating, 4. rounding decimals introduction packet -, 5. word problems involving rounding (yr6), 6. 1: rounding numbers, 7. rounding, decimal places and significant figures, 8. round each number to the nearest 1,000.

Worksheet on Rounding Off Number

In worksheet on rounding off number we will solve 10 different types of problems.

1. Round off to nearest 10 each of the following numbers: (a) 14 (b) 57 (c) 61 (d) 819 (e) 7729 2. Round off to nearest 100 each of the following numbers: (a) 5183 (b) 796 (c) 360 (d) 7254 (e) 49285

3. Round off to nearest 1000 each of the following numbers: (a) 3789 (b) 41338 (c) 89952 (d) 14239 (e) 79876 4. Round off to nearest 10000 each of the following numbers: (a) 16389 (b) 79838 (c) 17852 (d) 715259 (e) 559876 5. Round off to nearest 10 and 1000. (a) 62737 (b) 82990 (c) 289923 (d) 17437 (e) 53728 6. Round off to the nearest one (units place): (a) 57.326 (b) 8.808 (c) 290.752 (d) 1394.301 (e) 434.28 7. Round off to correct one place of decimal: (a) 99.39 (b) 7.84 (c) 375.34 (d) 72.645 (e) 83.38 8. Round off to correct two places of decimal: (a) 7.523 (b) 35.095 (c) 89.746 (d) 88.888 (e) 49.226

9. Divide 12.73 by 8 and round off correct to two decimal places. 10. Find the value of 200/33 up to one place decimal. To download the above worksheet Click Here.

● Rounding Numbers.

Round off to Nearest 10.

Round off to Nearest 100.

Round off to Nearest 1000.

Rounding off Decimal Fractions.

Correct to One Decimal Place.

Correct to Two Decimal Place.

Worksheet on Rounding off number.

5th Grade Numbers Page 5th Grade Math Problems 5th Grade Math Worksheets From Worksheet on Rounding Off Number to HOME PAGE

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Rounding Numbers

Rounding numbers means adjusting the digits of a number in such a way that it gives an approximate value. This value is an easier representation of the given number. For example, the population of a town could be easily expressed as 700,000 rather than 698,869. Rounding numbers makes calculations simpler, resulting in a figure that is easy to remember. However, rounding of numbers is done only for those numbers where the exact value does not hold that much importance.

Let us learn more about rounding numbers, to get a better idea of how to round off a number to the nearest ten, hundred, thousand, and so on.

What is Rounding Numbers?

Rounding a number means the process of making a number simpler such that its value remains close to what it was. The result obtained after rounding off a number is less accurate, but easier to use. While rounding a number, we consider the place value of digits in a number.

Let us understand the concept of rounding through an example. Susan covered a distance of 2.05 miles, which she noted as approximately 2 miles. How did she estimate the approximate value of the distance she covered? Why didn't she record her distance as 3 miles? Noting an approximate and simpler value for a given number helps to make the analysis and calculations easier while using that number. Here, Susan noted an easier value to keep a record of the distance travelled by her.

Numbers can be rounded to different digits, like, they can be rounded to the nearest ten, hundred, thousand, and so on. For example, 541 rounded to the nearest hundred is 500 because 541 is much closer to 500 than 600. While rounding a number, we need to know the answer to the question,' What are we rounding the number to?' Suppose we need to round the number 7456. When 7456 is rounded to the nearest ten, it becomes 7460, but when 7456 is rounded to the nearest thousand, then it becomes 7000. A few examples like these are given below.

Rounding Numbers to the Nearest Ten

Rounding numbers to the nearest ten means we need to check the digit to the right of the tens place, that is the ones place. For example, when we round the number 7486 to the nearest ten, it becomes 7490.

Rounding Numbers to the Nearest Hundred

Rounding numbers to the nearest hundred means we need to check the digit to the right of the hundreds place, that is, the tens place. For example, when 7456 is rounded to the nearest hundred, it becomes 7500.

Round-Up and Round-Down

While rounding is a generic term, we usually use the terms, 'round up' or 'round down' to specify if the number has increased or decreased after rounding. When the rounded number is increased, then the given number is said to be rounded up, whereas, if the rounded number is decreased, then it is said to be rounded down.

Rules for Rounding Numbers

How do we decide which value is more appropriate between different approximated values of a number? Should we choose a number greater than the given number or go with the smaller one?

We first need to know what our rounding digit is. This digit is the one that will ultimately be affected.
After this, we need to check the digit to the right of this place which will decide the fate of the rounding digit.
If the digit to the right is less than 5, we do not change the rounding digit. However, all the digits to the right of the rounding digit are changed to 0.
If the digit to the right is 5 or more than 5, we increase the rounding digit by 1, and all the digits to the right of the rounding digit are changed to 0.

a.) If the bill at a furniture store comes to $3257, what is the rounded value of the amount to the nearest ten?

b.) If the bill comes to $3284, what would be the rounded value of this amount to the nearest ten?

a.) $3257 needs to be rounded to the nearest ten. So, let us mark the digit in the tens place, which is 5. Now, let us check the number to the right, which is 7 in this case. Since 7 is more than 5, we will replace 5 with 6, and all the digits to the right will become 0. So, $3257 is rounded to $3260.

b .) Here, $3284 needs to be rounded to the nearest ten. So, let us mark the digit in the tens place, which is 8. Now, let us check the number to the right, which is 4 in this case. Since 4 is less than 5, 8 will remain unchanged and the remaining digits to the right will change to 0. So, $3284 is rounded to $3280.

How to Round Off Whole Numbers?

Whole numbers are rounded off by following the same rules mentioned above. Let us apply the rules with the help of an example.

Example: Round 7234 to the nearest hundred.

Step 1: Mark the place value up to which the number needs to be rounded. Here, 7234 needs to be rounded to the nearest hundred. So, we mark 2 which is in the hundreds place.
Step 2: Observe and underline the digit to the right of 2, that is the tens place. Here, it is 3, so we will mark it as: 7 2 3 4
Step 3: Compare the underlined digit with 5.
Step 4: If it is less than 5, all the digits towards its right including it will be replaced by 0 while the digit in the hundreds place (2) will remain unchanged. Therefore, 7234 will be rounded to 7200.

Note: If the number to the right of 2 was 5 or greater than 5, then all the digits to the right of 2 would become 0, and 2 would be increased by 1 changing it to 3. For example, if the given number was 7268, then it would be rounded up to 7300 (to the nearest hundred).

How to Round Off Fractions?

Fractions are numerical values that represent a part of a whole. They are written in the form of (p/q), where q is not equal to zero. A simple rule to round fractions to the nearest whole number is to compare proper fractions to 1/2. In case if it is an improper fraction, we need to change it to a mixed fraction and then compare the fractional part with 1/2. We round up the fraction if it is equal to or greater than 1/2, and we round down if it is less than 1/2. Let us understand rounding off fractions to the nearest whole number using the following example.

Example: Round the given fractions to the nearest whole number:

b.) $6 \dfrac{2}{5}$

a.) We can round off a proper fraction to the nearest whole number by following the simple rule of comparing it with 1/2. Since 3/4 is greater than 1/2, it will be rounded off to 1.

b.) $6 \dfrac{2}{5}$ is a mixed fraction. Here, we will keep the whole number part aside and compare the fractional part with 1/2. So, keeping 6 aside, we will check if 2/5 is greater than or less than 1/2. Since 2/5 is less than 1/2, we will round the given mixed fraction to 6.

c.) 21/5 is an improper fraction, so we will convert it to a mixed fraction. This will make it $4 \dfrac{1}{5}$. Now, we will keep the whole number part aside and compare the fractional part with 1/2. So, keeping 4 aside, we will check if 1/5 is greater than or less than 1/2. Since 1/5 is less than 1/2, we will round the given fraction to 4.

How to Round Off Decimal Numbers?

A decimal number is a combination of a whole number part and a fractional part separated by a decimal point. Rounding decimal numbers works in the same way as we round whole numbers although we need to know the decimal place values of all the digits in the given number. This refers to the digits given before the decimal point as well as the digits given after the decimal point. Observe the decimal place value chart to understand this better.

We usually round decimal numbers to the nearest tenths, hundredths, thousandths, and so on, which represent the place values after the decimal point. However, sometimes we even need to round a decimal to the nearest whole number. In this case, we check the tenths digit. If it is equal to or more than 5, then the given number is rounded up, and if the tenths digit is less than 5 then the given number is rounded down.

Example 1: Round 5.62 to the nearest whole number.

Solution: Since we need to round this decimal to the nearest whole number, we will check the tenths digit. In this case, the tenths digit is 6, which is more than 5. So, the number will be rounded to 6. In other words, 5.62 ≈ 6

In the other cases, where we need to round decimals to the nearest tenths, hundredths, or thousandths, we need to remember the simple rule of marking the number up to which we are rounding and checking the number to its right. For example, when we round decimal numbers to the nearest hundredths, we need to check the thousandths place. Similarly, if we need to round decimal numbers to the nearest tenths, we need to check the hundredths place. If the number to be checked is less than 5, then the rounding number remains unchanged, and the following digits are replaced with 0. Whereas, if the number to be checked is 5 or more than 5, then the rounding number is increased by 1 and the following digits are changed to 0. Let us understand this with an example.

Example 2: Round 0.439 to the nearest hundredths.

Solution: In this case, the digit to the right of the hundredths place, that is, the thousandths place is 9, which is more than 5. So, we will add 1 to the digit in the hundredths place, that is, 3 + 1 = 4, and write 0 in the digits to the right. So, 0.439 will be rounded to 0.44

Note: It should be noted that when we round a decimal number to the nearest hundredth, the round decimal fraction is said to be correct to two places of decimal. In other words, if we are asked to round off a number to two decimal places, it means we need to round it to the nearest hundredths. Similarly, when we are asked to round off a number to one decimal place, it means we need to round it to the nearest tenths .

Tips on Rounding Numbers:

The following tips are helpful in solving questions related to rounding numbers.

While rounding numbers, we always need to check the digit to the right of the rounding number. If it is less than 5, the rounding number remains the same and the following digits are changed to 0. If the digit to the right is equal to or more than 5, we increase the rounding digit by 1 and the following numbers are changed to 0.
When we round decimal numbers, we usually come across terms like round to the nearest tenths, hundredths, thousandths, and so on.
When we are asked to round off a number to one decimal place, it means we need to round it to the nearest tenths, similarly, when we are asked to round off a number up to two decimal places, it means we need to round it to the nearest hundredths.
When the rounded number is increased, then the given number is said to be rounded up, whereas, if the rounded number is decreased, then it is said to be rounded down.

Rounding Numbers Examples

Example 1: Round 321 to the nearest hundred, using the rules for rounding numbers.

While rounding numbers to the nearest hundred, we check the digit in the tens place. In this case, it is 2, which is less than 5. Therefore, this digit and all the digits to its right will change to 0 and the digit in the hundreds place will remain the same. Therefore, 321 is rounded to 300. This can be expressed as 321 ≈ 300.

Example 2: Using the rules of rounding numbers, round $6 \dfrac{1}{5}$ to the nearest whole number.

A mixed fraction is made up of a whole number part and a fractional part. When we round off mixed fractions to a whole number, we compare the fractional part with 1/2. In this case, 6 is the whole number part and 1/5 is the fractional part. Now, we will keep the whole number part aside and compare the fractional part with 1/2. So, keeping 6 aside, we will check if 1/5 is greater than or less than 1/2. Since 1/5 is less than 1/2, we will round the given fraction to 6. Therefore $6 \dfrac{1}{5}$ ≈ 6

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Practice Questions

Faqs on rounding numbers, what is rounding numbers in math.

Rounding a number means converting a number to a simpler value such that its value remains close to what it was. Rounding numbers makes calculation simpler and converts figures to an approximate value which is easier to remember. For example, if the population of a town is 692,769, it can be rounded to 700,000, and it would be easier to remember an approximate figure of 700,000 rather than the real figure.

What are the Rules for Rounding Off Decimal Numbers?

There are some basic rules that need to be followed for rounding decimal numbers. They are similar to rounding the other numbers, however, we need to know the decimal place values of all the digits in the given number. This refers to the digits given before the decimal point as well as the digits given after the decimal point. In other words, we usually round decimal numbers to the nearest tenths, hundredths, thousandths, and so on, which represent the place values after the decimal point. Sometimes, we even round the decimal to the nearest whole number. In all these cases, we use the following rules.

For example, if we need to round 0.476 to the nearest tenths, it means we will check the digit to its right, which is the hundredths digit. In this case, it is 7 which is more than 5. Therefore, 0.476 will be rounded up to 0.5 to the nearest tenths.

What is 62 Rounded to the Nearest ten?

When 62 is rounded to the nearest 10, we need to check the digit in ones place. Here, it is 2, which is less than 5. So, 6 will remain the same, and 2 will change to 0. Therefore, 62 rounded to the nearest ten will be 60.

Where do we Use Rounding of Numbers in Real Life?

In real life, we usually round numbers whenever the exact value is not so important. For example, if we want to know the approximate amount that we spent in a grocery store, or the amount while estimating a budget, or while expressing larger figures like the population of a town. We estimate the amount to simpler numbers so that calculation becomes easier. For example, if we know that our monthly expenditure would be around $590, we can easily round the number to $600 which is a figure that is easier to remember.

How to Round Numbers to the Nearest Tenth?

If we need to round decimal numbers to the nearest tenth, we need to check the digit to the right of the digit on the tenths place, which is the hundredths place. If the number in the hundredths place is less than 5, then the rounding number remains unchanged, and the following digits are replaced with 0. Whereas, if the number to be checked is 5 or more than 5, then the rounding number is increased by 1 and the following digits are changed to 0. For example, to round 56.73 to the nearest tenth, we will check the digit in the hundredths place, which is 3 in this case. Since 3 is less than 5, 7 will remain the same and the following digits will become 0. So, 56.73 rounded to the nearest tenths will become 56.7

What is the Purpose of Rounding Numbers?

Rounding numbers means adjusting the digits of a number such that it gives an estimated result. Rounding a number gives an approximate value which is a simpler and a shorter representation of the given number. For example, if the population of a town is 498,821, it would be easier if it is expressed as 500,000. This helps in making calculations easier with a figure that is easy to remember and note. However, rounding of numbers is done in those cases where the exact value does not hold that much importance.

What is Rounding Numbers to the Nearest Ten?

When we round numbers to the nearest ten, we first mark the digit in the tens place. Then, we observe the 'ones' place, which lies to the right of the tens column. According to the rules, if the digit in the ones place is 5 or more than 5, we add 1 to the digit in the tens place, that is, we increase the tens place by 1 and write 0 in all the digits to the right. However, If the digit in the ones place is less than 5, we write 0 in the ones place and in all the places to its right, and the digit in the tens place remains the same. For example, if we need to round 389 to the nearest ten, we will check the digit in ones place. In this case, it is 9 which is more than 5. So, 8 will change to 9, and 389 will be rounded to 390.

How to Round Numbers to the Nearest 100?

In order to round numbers to the nearest hundred, we need to check the digit to its right, which is the tens place. For example, if we need to round 3270 to the nearest 100, we will check the tens place. In this case, it is 7, which means the digit in the hundreds place will be increased by 1, that is, 2 will become 3 and the remaining digits to its right will become zero. Therefore, 3270 will be rounded up to 3300.

How to Round Numbers to the Nearest Thousand?

When we round numbers to the nearest thousand, we check the digit in the hundreds place. If the digit in the hundreds place is 5 or more than 5, we increase the thousands place by 1 and write 0 in all the digits to the right. In case, if the digit in the hundreds place is less than 5, we write 0 in the hundreds place and in all the places to its right, while the digit in the thousands place remains as it is. For example, let us round 76431 to the nearest thousand. We will first check the digit in the hundreds place. In this case, it is 4, which is less than 5. So, 6 will remain as it is and all the digits to the right will become 0. Therefore, 76431 will be rounded to 76000.

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Rounding – Definition with Examples

What do you mean by rounding off a number, example of rounding off from everyday life, how to round off different numbers, solved examples , practice problems, frequently asked questions.

Rounding off is nothing but estimation. Estimating the actual number to its nearby number is called rounding off.

Evaluate Algebraic Expressions with One Operation Game

When someone asks you the price of your book, you say 100 even if it is 98. This is giving an estimation after rounding off a number. This is how we apply the concept of rounding off in our everyday life.

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Different numbers use different ‘rounding off’ rules. Let’s discuss them one by one.

Whole Numbers

Whole numbers are rounded off at different place values.

Nearest Ten

Check the unit place digit:

If the unit place digit is less than 5 then keep the tens place digit the same and put 0 at the unit place.
If the unit place is 5 or more than 5 then change the tens digit into its successor and put 0 at the unit place.

Example:

If we round off 15,493 to the nearest tens place then the answer will be 15,490.

As the unit place is less than 5, the tens place digit will not change.

Similarly, if we round off 12,359 to its nearest tens place then the answer will be 12,360.

As the unit place is more than 5, the tens place digit will change its successor.

Nearest Hundred

Check the tens place digit:

If the tens place is less than 5 then keep the hundred place digit the same and put 0 at the tens and unit place.
If the tens place is 5 or more than 5 then change the hundred digit into its successor and put 0 at the tens and unit place.

If we round off 15,443 to the nearest hundred places then the answer will be 15,400. As the tens place is less than 5, the hundred place digit will not change.

Similarly, if we round off 12,359 to its nearest hundred places then the answer will be 12,400.

As the tens place is 5, the hundred place digit will change to its successor.

Nearest Thousand

Check the hundred place digit:

If the hundred place digit is less than 5 then keep the thousand place digit the same and put 0 at the hundred, tens, and unit place.
If the hundred place digit is 5 or more than 5 then change the thousand place digit into its successor and put 0 at the hundred, tens, and unit place.

If we round off 15,443 to the nearest thousand place digit then the answer will be 15,000. As the hundred place digit is less than 5, the thousand place digit will not change.

Similarly, if we round off 12,659 to its nearest thousand place digit then the answer will be 13,000.

As the hundred place digit is more than 5, the thousand place digit will change to its successor.

Decimal Number

The concept is quite similar to the whole number with some minor but noteworthy changes. If the digit right to the place value you are rounding to is less than 5, round down. However, if it’s 5 or more than 5, round up.

Nearest Whole

5.9165 rounded to the nearest whole is 6.

As 5 is followed by 9 and 9 is greater than 5. So, round up.

Nearest Tenth

5.9165 rounded to the nearest tenth is 5.9

As 9 is followed by 1 and 1 is smaller than 5. So, round down.

Nearest Hundredth

5.9165 rounded to the nearest hundredth is 5.92.

As 1 is followed by 6 and 6 is greater than 5. So, round up.

Nearest thousandth

5.9165 rounded to the nearest thousandth is 5.917.

As 6 is followed by 5. So, round up.

Example 1. Round off the following numbers to the nearest ten:

Solution 1.

5,499 rounded to the nearest ten is 5,500.

The unit place digit is more than 5 so add one to the tens place digit.

3,453 rounded to the nearest ten is 3,450.

The unit place digit is less than 5 so the tens place digit will remain the same.

4,405 rounded to the nearest ten is 4,410.

The unit place digit is 5 so add one to the tens place digit.

Example 2. Round off the following numbers to the nearest hundredth.

Solution 2.

2.656 rounded to the nearest hundredth is 2.66.

The digit next to the hundredth place digit is more than 5 so add 1 to the hundredth place digit.

2.305 rounded to the nearest hundredth is 2.31.

The digit next to the hundredth place digit is 5 so add 1 to the hundredth place digit.

3.234 rounded to the nearest hundredth is 3.23.

The digit next to the hundredth place digit is less than 5 so the hundredth place digit will remain the same.

Example 3. Round off the following numbers to the nearest thousand.

Solution 3.

44,590 rounded to the nearest thousand is 45,000.

The hundred place digit is 5 so add 1 to the thousand place digit.

66,235 rounded to the nearest thousand is 66,000.

The hundred place digit is less than 5 so keep the thousand place digit the same as before.

Rounding off

Attend this Quiz & Test your knowledge.

A number rounded to the nearest 10 is 500. What could be the possible number?

Simplify the following after rounding off each number to the nearest hundred 45,789 + 23,848 + 66,321 – 34,213, match the numbers with their round off to the nearest tens..

$Rounding – Definition with Examples$

Can we round off lengths and heights?

Yes. Heights and lengths can be rounded off.

What is 9,999 rounded off to the nearest hundred?

If we round off 9,999 to the nearest hundred, we will get 10,000.

Are round-off figures exact?

No. Round-off figures are not exact but are in proximity to the exact figure.

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Rounding To The Nearest Tens – Definition, Examples, FAQs
Even Numbers and Odd Numbers – Properties, Examples
Rounding Decimals – Definition with Examples
Multiplying Decimals – Definition with Examples

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Rounding Off Numbers – Definition, Rules, Examples | How to Round Numbers to Nearest Ten, Hundred?

Rounding off numbers is an approximation that is used in our everyday life. It means it is a number that makes your calculations simpler by keeping the value closer to the next number. There are some rules for rounding off the numbers. Scroll down this page to know the rules for rounding off numbers. Rounding off numbers or significant figures is the basic concept that your child needs to learn at the primary level itself. Make your calculations easy by adjusting the number to the nearest values.

Rounding Off Numbers – Definition

Rounding off is a process in which we make the number simple by keeping its value intact and closer to the next number. We can perform rounding off operations for decimal numbers, whole numbers, and so on. Rounding Off can be done at various places such as tens, hundreds, thousands, and so on. For Example 34.67 can be rounded to tens place is 34.7 i.e. hundreds place 7 is greater than 5 so we will increase the tens place by 1.

Rules in Rounding Off Numbers

In order to make your problems easy, you need to follow some rules to round off the numbers. Go through the below section to know the rules for rounding numbers.

If the digit to be dropped while rounding off is 5 or greater than 5, the following digit is increased by 1.
If the digit to be dropped while rounding off is less than 5, the following digit is left unchanged.
All the zeros that are between non-zero digits are significant.
While rounding off a digit at a higher place value, we ignore the lower place value digits.
All the non-zero digits in the number are significant.
The zeros on the right of a non-zero digit in a whole number are significant.
Rounding Decimals
Rounding Decimals to the Nearest Tenths
Rounding Decimals to the Nearest Hundredths
Rounding Decimals to the Nearest Whole Number

Rounding Off Whole Numbers

Follow the step-by-step process listed below to become familiar with the concept of Rounding Whole Numbers. They are as such

1. To get the accurate value, always choose the smaller value in the unit’s place. 2. The digit previous to this place should be compared with 5. 3. If it is less than 5, all the digits towards its left will be replaced by 0. 4. If it is greater than 5, all the digits towards its left will be replaced by 0.

Rounding Off Decimal Numbers

Know the simple process for rounding off decimal numbers and estimate the nearest values easily. They are as under

1. If the digits at the righthand side are less than 5, consider them as equal to zero. 2. If the digits at the righthand side are greater than or equal to 5, then add +1 to that digit.

Types of Rounding Off Numbers

Rounding Numbers can be of different types such as rounding to nearest tens, hundreds, thousands, and so on. They are along the lines

1. Rounding Off Number Nearest to Ten: First, identify the digit present in the tens place. And then identify the next smallest place in the number. If the number in the smallest place is less than 5, then round up the digit. Example: The round-off number 78 nearest to ten is 80. Because 8 is greatest than 5 so we can add to the tens place and the unit’s place will be 0.

2. Rounding Off Number Nearest to Hundred: First, identify the digit present in the hundreds place. And then identify the next smallest place in the number. If the number in the smallest place is less than 5, then round up the digit. Example: The round-off number 789 nearest to hundred is 800.

3. Estimation of Sum or Difference: The first step in estimating a sum or a difference is to round the numbers, by changing them to the nearest power of ten, hundred, thousand, etc. Round the numbers first, then use mental math to estimate an answer.

Rounding Off Numbers Examples

Example 1. We have the numbers 212 and 301. Write the roundoff number nearest to a hundred? Solution: 212 is closer to 200 and 301 is closer to 300. So, the number nearest to hundred is 200 and 300. Example 2. Round off to the nearest 10 in each of the following numbers: a. 17 b. 38 c. 71 d. 68 Solution: First, identify the digit present in the tens place. And then identify the next smallest place in the number. If the number in the smallest place is less than 5, then round up the digit. a. 7 is greater than 5 so we should add 1 to the next digit. The number closer to 17 is 20. b. 8 is greater than 5 so we should add 1 to the next digit. The number closer to 38 is 40. c. 1 is less than 5 so the unit place remains 0. The number closer to 71 is 70. d. 8 is greater than 5 so we should add 1 to the next digit. The number closer to 68 is 70.

Example 3. Estimate the sum of 810 and 99 by using the mental math that can be rounded to the nearest hundred. Solution: 810 can be written as 800 99 can be written as 100 800 + 100 = 900

Example 4. Estimate the sum of 717 and 102? Solution: 717 > 700 717 can be rounded off to 700 102 can be rounded off to 100 700 + 100 = 800

Example 5. Estimate 4986 and 2894? Solution: 4986 can be rounded off to 5000. 2894 can be rounded off to 3000. 5000 + 3000 = 8000

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What is Rounding off Numbers and How to Round Numbers?

We can use linear equations in our day-to-day life, for example, when comparing rates, making predictions, budgeting, and more. An equation is said to be linear when all the variables have the highest power equal to one. The variables are dependent on one another. This type of equation is also called a one-degree equation. Read on to discover the linear equation standard form, formula, graph, and guidelines to solve a linear equation in one or two variables.

Here is what we will cover in the article:

What is a linear equation ?
Linear equation standard form
Linear equation graph
Linear equations in one variable
Linear equations in two variables
How do solve linear equations?

What is a Linear Equation?

An equation with the highest degree of 1 is linear. It has no variable with an exponent of more than 1. A linear equation always forms a straight line on a graph, and thus, it gets its name ‘linear equation’.

In Mathematics, we have linear equations in one variable and two variables. The following examples will help you learn how to differentiate linear equations from nonlinear ones.

Linear Equation Formula

The linear equation formula expresses a linear equation. There are different ways a linear equation can be expressed. For example, we have the standard form, the point-slope form, or the slope-intercept form.

Linear Equations in Standard Form

The standard form of linear equations in one variable can be given as follows:

The terms in the above equation denote:

A and B are real numbers
x is the single variable

The standard form of linear equations in two variables can be given as follows:

Ax + By = C

A B and C are real numbers.
A is the coefficient of x
B is the coefficient of y
C is constant
x and y are the variables

Linear Equation Graph

On graphing a linear equation in one variable x, we get a vertical line parallel to the y-axis. If we graph a linear equation in two variables, x, and y, it forms a straight line. To graph, a linear equation, follow the steps given below.

Step 1: Note down your linear equation and convert it into the form of y = mx + b.
Step 2: When we have our equation in this form, we can replace the value of x for various numbers. We will get the resulting value of y, and we can create the coordinates.
Step 3: Next, we will list the coordinates in tabular form.
Step 4: Finally, we will plot the coordinates on a graph. Join the points to get a straight line. This line will represent our linear equation.

How to Solve Linear Equations?

The main goal of solving an equation is to balance the two sides. An equation resembles a weighing balance as we have to ensure that both sides weigh equally. So, if we add a number on one side, we must add it to the other side as well.

Similarly, if we divide or multiply a number on the left-hand side, we will do the same for the right-hand side. To solve a linear equation, we will bring the variables to one side and keep the constant on the other side. Then we will find the value of the unknown variable.

Tips on Solving Linear Equations:

The solution or root of the linear equation is the value of the variable. It makes a linear equation true.
This solution remains unaffected if the same number is multiplied, added, subtracted, or divided for both sides of the equation.
On graphing a linear equation in one or two variables, we get a straight line.

Solution of Linear Equations in One Variable

We need to create a balance on both sides of the linear equation to solve it. The equality sign symbolizes that the expressions are equal on the two sides. The following sample linear equation will help you understand the steps of solving the linear equation in one variable.

Example 1 : Solve (2x – 4)/2 = 3(x – 1)

Step 1 : We will clear the fraction

x – 2 = 3(x – 1)

Step 2 : We will simplify the two sides of the equations by opening the brackets and multiplying the number by the inner terms of the bracket.

x – 2 = 3x – 3

Step 3 : Next, we will isolate x

3-2 = 3x – x

Solution of Linear Equations in Two Variables

There are several methods for solving a linear equation in 2 variables. Some commonly used methods are:

Method of substitution
Cross multiplication method
Method of elimination

Substitution Method

We use the substitution method when we have two linear equations with two unknown values. The following steps will help you solve the linear equations.

Step 1: First, simplify the given equation. Expand the parenthesis.
Step 2: Now, we will solve one of the equations to obtain the value of either x or y.
Step 3: Substitute the value of x in terms of y in the other equation or the value of y in terms of x.
Step 4: Solve the new equation following the basic arithmetic operations rules (BODMAS/ DMAS) to find the value of a variable.
Step 5: Finally, use the value obtained and find the value of the second variable.

Example 2: Calculate the value of x and y from the equations 2x+3y = 13 and x-2y = -4

2x + 3y = 13 —————— (i)

x-2y = -4 ———————– (ii)

Solving eq (ii)

Substituting the value of x in eq ( i)

2 ( 2y -4) + 3y = 13

4y -8 + 3y =13

Substituting the value of y in eq (ii)

x= 2 (3) -4

Cross Multiplication Method

Cross multiplication is one of the simplest methods, and it is applicable only when we are given a pair of linear equations in two variables. We multiply the numerator of one fraction to the denominator of the other. The denominator of the first term is multiplied by the numerator of another term. The following equation is for solving linear equations in two variables using the cross multiplication method.

Elimination Method

The following steps will help you solve a linear equation:

Step 1: First, we will multiply the given equations with non-zero constants. This process makes the coefficients of any one of the variables numerically equal.
Step 2 : Next, we will add or subtract one equation from the other. This step will eliminate one variable. Now, we will get an equation in one variable.
Step 3: We can now solve the equation in one variable and get its value.
Step 4: Once we have the value of a variable, we can substitute this value in any one of the equations to calculate the other variable.

Example 3: Solve the following equations for x and y

2x+3y=6 —————— (i)

-2x+5y=10 —————-(ii)

We will add the two equations as follows

2x + 3y -2x +5y =6 +10

Since the coefficients of x are equal and opposite in sign, they will be eliminated.

Now, we will substitute the value of y in eq (i)

2x + 3(2) =6

Example 4 : If the difference in the measures of the given two complementary angles is 22°. Find the measure of the two angles.

Solution: Let the angle be x. The complement of x = 90 – x

Given their difference = 22°

Therefore, (90 – x) – x = 22°

⇒ 90 – 2x = 22

⇒ -2x = 22 – 90

⇒ -2x = -68

The complementary angle will be 90 -34 = 56

Answer: The two complementary angles are 56 and 34.

Practice Problems

Practice the following problems on linear equations to ace these questions in your examinations.

Question 1 : Solve the following linear equations using the substitution method.

4x-3y=20 and 16x-6y=80
2x-5y=10 and 3x+8y=15

Question 2 : Solve linear equations given below using the elimination method.

3x + y = 6 and 2x + 7y = 10.
4x + 2y = 5 and 4x + 6y =15

Question 3 : The sum of two numbers is 55. Suppose one number exceeds the other by 8. Find the two numbers.

Question 4: The length of a rectangle is thrice its breadth. If the perimeter of the rectangle is 32 meters, find the length and breadth of the rectangle.

Question 5 : James is five years younger than Lily. Four years later, Lily will be twice as old as James. What is their present age of James?

Question 6 : The cost of three tables and two chairs is $605. If the table costs $50 more than the chair, what are the costs of the table and the chair?

Frequently Asked Questions

1. how to properly round numbers.

Ans. Rounding a number is a pretty common task, and it’s one that people often get wrong. Here’s how to do it right:

If the number ending in .5 is greater than or equal to 5, round up.

If the number ending in .5 is less than 5, but greater than or equal to zero, round down.

If the number ending in .5 is less than zero, round up.

2. When to round up numbers?

Ans. When you’re rounding up numbers, you have to make sure that you’re rounding them up appropriately. If the number is less than or equal to 5, round it down. If the number is greater than 5 but less than or equal to 10, round it up. If the number is greater than 10, round it up.

3. What are the rules in rounding off numbers?

Ans. Rounding off numbers is a fairly simple process. Here are the rules:

-If the number ends in 5, round up.

-If the number ends in 0, round up.

-If there are any remaining digits, round down.

4. What is the procedure for rounding off numbers?

Ans. Rounding off numbers is a simple process that you can use to make your calculations easier to understand. It’s the process of taking a number and removing some portion of it so that the result is closer to an integer. For example, say you have the number 45.5. To round it off, you would take half of 45 (22) and then add it back onto the number 45.5—this gives you 45.75, which is closer to an integer than 45.5 was before rounding occurred.

5. Should 5 be rounded up or down?

Ans. 5 should be rounded up. This is because if you round 5 down, you’ll lose one of the zeros that make it so special. You don’t want that.

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Units Of Measurement
Error Significant Figures Rounding Off

Rounding Off Significant Figures

Rounding off is a type of estimation. Estimation is used in everyday life and also in subjects like Mathematics and Physics. Many physical quantities like the amount of money, distance covered, length measured, etc are estimated by rounding off the actual number to the nearest possible whole number.

What is Rounding Off?

Rounding off means a number is made simpler by keeping its value intact but closer to the next number. It is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc. Rounding off numbers is done to preserve the significant figures . The number of significant figures in a result is simply the number of figures that are known with some degree of reliability.

The number 13.2 is said to have 3 significant figures. Non-zero digits are always significant. 3.14159 has six significant digits (all the numbers give you useful information). Thus, 67 has two significant digits, and 67.3 has three significant digits.

Rounding Rules for Whole Numbers

Rounding rules for whole numbers are as follows:

To get an accurate final result, always choose the smaller place value.
Look for the next smaller place which is towards the right of the number that is being rounded off. For example, if you are rounding off a digit from the tens place, look for a digit in the one’s place.
If the digit in the smallest place is less than 5, then the digit is left untouched. Any number of digits after that number becomes zero and this is known as rounding down.
If the digit in the smallest place is greater than or equal to 5, then the digit is added with +1. Any digits after that number become zero and this is known as rounding up.

Rounding Rules for Decimal Numbers

Rounding rules for decimal numbers are as follows:

Determine the rounding digit and look at its righthand side.
If the digits on the right-hand side are less than 5, consider them as equal to zero.
If the digits on the right-hand side are greater than or equal to 5, then add +1 to that digit and consider all other digits as zero.

Learn more about errors in arithmetic operation here.

Example of How to Round Off

Round to nearest hundred.

Let’s consider the number 3350. To round off to the nearest significant number, consider hundreds places and follow the steps given below:

Identify the digit present in the hundreds place: 3
Identify the next smallest place in the number: 5
If the smallest place digit is greater than or equal to 5, then round up the digit.
Now add +1 to the digit in the hundreds place. 3+1=4. Therefore, the other digits become zero.
So the final number is 3400.

Round to Nearest Ten

Let’s consider the number 313.5. To round off to the nearest significant number, consider tens place and follow the steps as given below:

Identify the digit present in the tens place: 1
Identify the next smallest place in the number: 3
Since the digit in the smallest place is less than 5, a round down has to be done and also the digit remains unchanged.
Every other digit becomes zero.
So the final number is 310.

Let’s consider the number 499. To round off to the nearest significant number, consider tens place and follow the steps as given below:

Identify the digit present in the tens place: 9
Identify the next smallest place in the number: 9
As the digit in the one place is greater than 5, +1 has to be added.
Therefore, 9+1=10 and the 1 is carried to the next place.
So the final number is 500.

Round to Nearest Tenth

Let’s consider the number 0.73. To round off to the nearest significant number, consider tenths place and follow the steps as given below:

Identify the digit present in the tenth place: 7
If the smallest place digit is greater than or equal to 5 then round up the digit.
As the digit in the smallest digit is less than 5, the digit gets round down.
So the final number is 0.7

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Frequently Asked Questions – FAQs

What is meant by rounding off, how does rounding off work for whole numbers.

Look for the next smaller place, which is towards the right of the number that is being rounded off. For example, if you are rounding off a digit from the tens place, look for a digit in the one place.
If the digit in the smallest place is less than 5, then the digit is left untouched. Any number of digits after that number becomes zero, and this is known as rounding down.
If the digit in the smallest place is greater than or equal to 5, then the digit is added with +1. Any digits after that number become zero, and this is known as rounding up.

How to round off decimals?

Find the rounding digit and analyse it at its right-hand side.
If the digits on the right-hand side are less than 5, consider them equal to zero.

Explain the process of rounding the nearest tenth?

Define significant figures., is rounding off important.

Put your understanding of this concept to test by answering a few MCQs. Click ‘Start Quiz’ to begin!

Select the correct answer and click on the “Finish” button Check your score and answers at the end of the quiz

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Course: 5th grade > Unit 1

Rounding decimals on the number line
Round decimals using a number line
Worked example: Rounding decimals to nearest tenth
Round decimals
Understand decimal rounding
Rounding decimals word problems

Round decimals word problems

Decimal place value: FAQ
(Choice A) 111.25 ‍ A 111.25 ‍
(Choice B) 124.9 ‍ B 124.9 ‍
(Choice C) 115.95 ‍ C 115.95 ‍

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1.11: Rounding Off Numbers

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Learning Objectives

Use significant figures correctly in arithmetical operations.

Before dealing with the specifics of the rules for determining the significant figures in a calculated result, we need to be able to round numbers correctly. To round a number, first decide how many significant figures the number should have. Once you know that, round to that many digits, starting from the left. If the number immediately to the right of the last significant digit is less than 5, it is dropped and the value of the last significant digit remains the same. If the number immediately to the right of the last significant digit is greater than or equal to 5, the last significant digit is increased by 1.

Consider the measurement $207.518 \: \text{m}$. Right now, the measurement contains six significant figures. How would we successively round it to fewer and fewer significant figures? Follow the process as outlined in Table $\PageIndex{1}$.

Notice that the more rounding that is done, the less reliable the figure is. An approximate value may be sufficient for some purposes, but scientific work requires a much higher level of detail.

It is important to be aware of significant figures when you are mathematically manipulating numbers. For example, dividing 125 by 307 on a calculator gives 0.4071661238… to an infinite number of digits. But do the digits in this answer have any practical meaning, especially when you are starting with numbers that have only three significant figures each? When performing mathematical operations, there are two rules for limiting the number of significant figures in an answer—one rule is for addition and subtraction, and one rule is for multiplication and division.

In operations involving significant figures, the answer is reported in such a way that it reflects the reliability of the least precise operation. An answer is no more precise than the least precise number used to get the answer.

Rules for Calculations With Measured Numbers

How are significant figures handled in calculations? It depends on what type of calculation is being performed.

Multiplication and Division

For multiplication or division, the rule is to count the number of significant figures in each number being multiplied or divided and then limit the significant figures in the answer to the lowest count. An example is as follows:

The final answer, limited to four significant figures, is 4,094. The first digit dropped is 1, so we do not round up.

Scientific notation provides a way of communicating significant figures without ambiguity. You simply include all the significant figures in the leading number. For example, the number 450 has two significant figures and would be written in scientific notation as 4.5 × 10 2 , whereas 450.0 has four significant figures and would be written as 4.500 × 10 2 . In scientific notation, all significant figures are listed explicitly.

Example $\PageIndex{1}$

Write the answer for each expression using scientific notation with the appropriate number of significant figures.

23.096 × 90.300
125 × 9.000

Addition and Subtraction

If the calculation is an addition or a subtraction, the rule is as follows: limit the reported answer to the rightmost column that all numbers have significant figures in common. For example, if you were to add 1.2 and 4.71, we note that the first number stops its significant figures in the tenths column, while the second number stops its significant figures in the hundredths column. We therefore limit our answer to the tenths column.

1.2 plus 4.41 equals 5.61, which should be rounded to the tenths column as 5.6

We drop the last digit—the 1—because it is not significant to the final answer.

The dropping of positions in sums and differences brings up the topic of rounding. Although there are several conventions, in this text we will adopt the following rule: the final answer should be rounded up if the first dropped digit is 5 or greater and rounded down if the first dropped digit is less than 5.

77.2 plus 10.46 equals 87.66, which should be rounded to the tenths column as 87.7

Example $\PageIndex{2}$

13.77 + 908.226
1,027 + 611 + 363.06

Exercise $\PageIndex{2}$

217 ÷ 903
13.77 + 908.226 + 515
255.0 − 99
0.00666 × 321

Remember that calculators do not understand significant figures. You are the one who must apply the rules of significant figures to a result from your calculator

Example $\PageIndex{3}$

2(1.008g) + 15.99 g
137.3 s + 2(35.45 s)
$ {118.7 g \over 2} - 35.5 g $

Exercise $\PageIndex{3}$

Complete the calculations and report your answers using the correct number of significant figures.

5(1.008s) - 10.66 s
99.0 cm+ 2(5.56 cm)
If the number to be dropped is greater than or equal to 5, increase the number to its left by 1. e.g. 2.9699 rounded to three significant figures is 2.97
If the number to be dropped is less than 5, there is no change. e.g. 4.00443 rounded to four sig. figs. is 4.004
The rule in multiplication and division is that the final answer should have the same number of significant figures as there are in the number with the fewest significant figures.
The rule in addition and subtraction is that the answer is given the same number of decimal places as the term with the fewest decimal places.

Contributions & Attributions

This page was constructed from content via the following contributor(s) and edited (topically or extensively) by the LibreTexts development team to meet platform style, presentation, and quality:

Marisa Alviar-Agnew ( Sacramento City College )

Henry Agnew (UC Davis)

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Mathematics > Combinatorics

Title: on off-diagonal hypergraph ramsey numbers.

Abstract: A fundamental problem in Ramsey theory is to determine the growth rate in terms of $n$ of the Ramsey number $r(H, K_n^{(3)})$ of a fixed $3$-uniform hypergraph $H$ versus the complete $3$-uniform hypergraph with $n$ vertices. We study this problem, proving two main results. First, we show that for a broad class of $H$, including links of odd cycles and tight cycles of length not divisible by three, $r(H, K_n^{(3)}) \ge 2^{\Omega_H(n \log n)}$. This significantly generalizes and simplifies an earlier construction of Fox and He which handled the case of links of odd cycles and is sharp both in this case and for all but finitely many tight cycles of length not divisible by three. Second, disproving a folklore conjecture in the area, we show that there exists a linear hypergraph $H$ for which $r(H, K_n^{(3)})$ is superpolynomial in $n$. This provides the first example of a separation between $r(H,K_n^{(3)})$ and $r(H,K_{n,n,n}^{(3)})$, since the latter is known to be polynomial in $n$ when $H$ is linear.

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Rounding Numbers Worksheet
Online Rounding Practice Zone. In our Rounding Practice zone, you can practice rounding a range of numbers. You can round numbers to the nearest 10, 100 or even 1000. Want to round numbers to the nearest decimal place, you can do that too! Select the numbers you want to practice with, and print out your results when you have finished.
Round whole numbers word problems (practice)
Course: 4th grade > Unit 2. Lesson 1: Rounding whole numbers. Addition, subtraction, and estimation: FAQ. Rounding whole numbers to nearest hundred. Rounding whole numbers to nearest thousand. Round whole numbers. Rounding whole numbers: missing digit.
Rounding Word Problems (printable, online, answers)
Rounding Word Problems Worksheets. In these free math worksheets, students practice how to use rounding to estimate and check the answers to word problems. ... Step 2: Round any numbers given in the problem to the nearest whole number, or to the nearest ten, hundred, or thousand, depending on the level of accuracy needed. Step 3: Use mental ...
Rounding Worksheets
Grade 5 rounding worksheets. Rounding numbers to the nearest 10 within 0-10,000. Rounding numbers to the nearest 100 within 0-1,000,000. Rounding numbers to the nearest 1,000 within 0-1,000,000. Mixed rounding - round to the underlined digit (up to nearest million) Estimating and rounding word problems.
1.3: Rounding Whole Numbers
Note the digit to the immediate right of the round-off digit. If it is less than 5, replace it and all the digits to its right with zeros. Leave the round-off digit unchanged. ... Use the method of rounding whole numbers to solve each problem. Round 3387 to the nearest hundred. Answer. 3400. Practice Set A. Round 26,515 to the nearest thousand ...
Rounding Numbers
How to Round Numbers. Decide which is the last digit to keep. Leave it the same if the next digit is less than 5 (this is called rounding down) But increase it by 1 if the next digit is 5 or more (this is called rounding up) Example: Round 74 to the nearest 10. We want to keep the "7" (it is in the 10s position)
Rounding Off Numbers Problem Solving Worksheets
Rounding Off Numbers Problem Solving - Displaying top 8 worksheets found for this concept.. Some of the worksheets for this concept are Lesson plan rounding off, Rounding, Problem solving rounding and estimating, Rounding decimals introduction packet, Word problems involving rounding yr6, 1 rounding numbers, Rounding decimal places and significant figures, Round each number to the nearest 10.
Rounding whole numbers word problems (video)
In order to round to the hundreds place, you have to look at the tens place to decide whether to round up or down. If the number in the tens place is between 0 and 4, you round down: - ones place becomes 0. - tens place becomes 0. - hundreds place stays the same. If the number in the tens place is between 5 and 9, you round up:
Worksheet on Rounding Off Number
In worksheet on rounding off number we will solve 10 different types of problems. 1. Round off to nearest 10 each of the following numbers: 2. Round off to nearest 100 each of the following numbers: 3. Round off to nearest 1000 each of the following numbers: 4. Round off to nearest 10000 each of the following numbers:
Math Practice Problems
Round each number to the nearest thousand. Example: 5689 → 6000. Learn more about our online math practice software . "MathScore works." Developed by MIT graduates, MathScore provides online math practice for Rounding Numbers and hundreds of other types of math problems.
Rounding Practice Questions
The Corbettmaths Practice Questions on Rounding. Previous: Similar Shapes Area/Volume Practice Questions
Rounding Numbers
Example 2: Using the rules of rounding numbers, round $6 \dfrac{1}{5}$ to the nearest whole number. Solution. A mixed fraction is made up of a whole number part and a fractional part. When we round off mixed fractions to a whole number, we compare the fractional part with 1/2. In this case, 6 is the whole number part and 1/5 is the fractional ...
What is Rounding Off Numbers in Math? How to do a Round Off (Definition
Solution: To round 1599 to the nearest thousand, the rounding digit at the place of thousand is 1. The digit to the right of the rounding digit is 5. This indicates that we have to increase the thousands-place digit by 1 and replace the other digits with zeros. We can conclude that $1599 rounded to the nearest thousand is $2000.
What is Rounding Numbers? Rules, Definition, Examples, Facts
Round off the following numbers to the nearest ten: 5499. 3,453. 4,405. Solution 1. 5,499 rounded to the nearest ten is 5,500. The unit place digit is more than 5 so add one to the tens place digit. 3,453 rounded to the nearest ten is 3,450. The unit place digit is less than 5 so the tens place digit will remain the same.
Rounding Off Numbers
The round-off number 789 nearest to hundred is 800. 3. Estimation of Sum or Difference: The first step in estimating a sum or a difference is to round the numbers, by changing them to the nearest power of ten, hundred, thousand, etc. Round the numbers first, then use mental math to estimate an answer. Rounding Off Numbers Examples. Example 1 ...
Rounding Off Numbers: Rules, Applications & Examples
Rounding off numbers means simplifying a number by keeping its value closer to the next number. We can round numbers to the nearest whole numbers, or we can also round decimals. ... Introduction: We can find the solution to the word problem by solving it. Here, in this topic, we can use 3 methods to find the solution. 1. Add using counters 2 ...
Rounding Off
Rounding off means a number is made simpler by keeping its value intact but closer to the next number. It is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc. Rounding off numbers is done to preserve the significant figures. The number of significant figures in a result is simply the number of figures ...
1.11: Rounding Off Numbers
The calculator answer is 921.996, but because 13.77 has its farthest-right significant figure in the hundredths place we need to round the final answer to the hundredths position. Because the first digit to be dropped (in the thousandths place) is greater than 5, we round up to 922.00. 922.00 = 9.2200 ×102 922.00 = 9.2200 × 10 2.
Round decimals word problems (practice)
Rounding decimals on the number line. Round decimals using a number line. Worked example: Rounding decimals to nearest tenth. Round decimals . Understand decimal rounding. Rounding decimals word problems. Round decimals word problems. Decimal place value: FAQ. Math > 5th ... Learn for free about math, art, computer programming, economics ...
1.11: Rounding Off Numbers
Answer. The calculator answer is 921.996, but because 13.77 has its farthest-right significant figure in the hundredths place we need to round the final answer to the hundredths position. Because the first digit to be dropped (in the thousandths place) is greater than 5, we round up to 922.00. 922.00 = 9.2200 × 102. b.
[2404.02021] On off-diagonal hypergraph Ramsey numbers
Title: On off-diagonal hypergraph Ramsey numbers Authors: David Conlon , Jacob Fox , Benjamin Gunby , Xiaoyu He , Dhruv Mubayi , Andrew Suk , Jacques Verstraete View a PDF of the paper titled On off-diagonal hypergraph Ramsey numbers, by David Conlon and 6 other authors

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1.3: Rounding Whole Numbers

Rounding as an Approximation

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Exercises for Review

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Common Method

How to Round Numbers

Example: Round 74 to the nearest 10

Example: Round 86 to the nearest 10

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Rounding Decimals

3.1416 rounded to hundredths is 3.14

3.1416 rounded to thousandths is 3.142

1.2735 rounded to tenths is 1.3

1.2735 rounded to 3 decimal places is 1.274

Rounding Whole Numbers

134.9 rounded to tens is 130

12,690 rounded to thousands is 13,000

15.239 rounded to ones is 15

Rounding to Significant Digits

1.239 rounded to 3 significant digits is 1.24

134.9 rounded to 1 significant digit is 100

0.0165 rounded to 2 significant digits is 0.017

Rounding Off Numbers Problem Solving

1. LESSON PLAN: Rounding off

Worksheet on Rounding Off Number

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